Hydrologie record analysis

The connections between channel network parameters and the hydrologie response o f a basin in the form o f the outflow hydrograph were first recognised by Rodriguez- Iturbe and Valdes (1979). They pioneered the Géomorphologie Unit Hydrograph (GUH) which has as its basis the description o f the ordered drainage system by statistical laws. They expressed the instantaneous unit hydrograph (lUH) as a function of Horton’s numbers Rg (bifurcation ratio), R^ (basin area ratio), Rg (stream length ratio), the watershed order Q, and the Xi (a mean waiting time for each stream order Q). This means that the structure o f the hydrologie response is intimately linked to the géomorphologie parameters o f the basin, provided that the link between the character of the GIUH and the network measures is constant between basins. The most important characteristics o f an lUH are the peak discharge qp (m^ sec'^) and the time to peak tp (sec) which are calculated through the relations

qp = 0v (2.1)

where v is water velocity (m sec'^) and 0 and k are expressed through the following two basic general equations:

9 = 1 .3 1 /L n R L ‘’‘'^ (2.3)

k = 0.44LnRB“ ” RA'“ “ RL'"’* (2.4)

where Lq is the mean length (km) of streams o f order Q.

Based on these premises, it is reasonable to expect that a relationship linking flow duration and processes upstream can be derived from catchment geomorphology. What makes the GIUH unique is that it is derived from considerations of drainage network structure, and is essentially rooted in empirical geomorphic laws, since it represents in mathematical terms the probability density function of a water particle following a certain path through the overland catchment regions and channels before arriving at the basin outlet. Thus the GIUH quantifies the characteristics o f runoff generation in the catchment outlet. In that way, a link is established between climate, the géomorphologie structure and the hydrologie response of any basin.

The idea that the hydrologie response at the basin scale should only depend on some of the gross features of a basin and not on the details o f its channel network geometry appears to begin with Lienhard (1964). It gained further credibility later on (Surkan, 1969; Lee and Delleur, 1976; Boyd et al., 1979). However, as was noted very early in some empirical studies (e.g. Morisawa, 1962), Horton’s bifurcation ratio Rb alone has little, if any influence on the important hydrologie properties

playing a role in the response o f a basin. According to Gupta et al., (1980), there seem to be severe shortcomings in any attempt to use Strahler ordered streams for understanding the structure of the hydrologie response of a network, the most important being the loss of information about network shape. Moreover, they criticised the implementation o f the GIUH on the grounds that it does not take into consideration the topologic properties of the network. Another limitation of the

GIUH is that the travel time distributions in each state are assumptions within the theory without any underlying basis for the actual physical response o f each channel (Gupta and Waymire, 1983). They managed to derive an analytical formulation of the network response without using Strahler ordered streams to define travel paths. Snell and Sivapalan (1994) further criticised the GIUH for its failure to incorporate the dynamic properties of the drainage network.

Despite these obvious failings o f the GIUH to provide insights into the differences between tree-like channel networks in a river basin over long periods of time, the unit hydrograph will be calculated from the different topographic map blue line networks. Moreover, the derived GIUH for different network configurations can be compared against the calculated network width function and link concentration function to provide a measure o f network sensitivity to its evolving underlying structure. This analysis may thus reveal how sensitive the network is to a combination o f climatic and land-use changes.

Almost half the total stream length of a drainage basin is made up of first-order tributaries which are the fundamental energy cells o f the drainage system (Leopold et al., 1964). They indicated that first order channels may directly drain approximately 80% of a drainage basin. Despite the importance o f fluctuations in the position o f stream sources to such indices as drainage density and texture, few studies have been made of the behaviour of first-order streams. Horton (1945) showed that the location of stream tips was related to a critical distance fi*om the divide at which the hydraulic power o f overland flow was sufficient to erode a channel. Others (e.g. Kirkby and Chorley, 1967) emphasised the relationship between the position o f stream heads and the distribution o f throughflow. However, nobody has attempted to examine changes in the location o f stream sources within a watershed, or even a number of them in relation to a changing hydrologie regime. The comprehensive model for stream network evolution on the catchment level presented in this thesis will provide firesh insights into the mechanisms governing channel network response over decadal and century timescales.

By using the appropriate geomoiphological indices calculated from the available fluvial networks, as they are represented in the various editions o f the maps available, the GIUH shall be derived for individual sub-basins that present the most interest in terms of the channel networks developed within their boundaries. It is anticipated that certain differences either in the shape of the derived hydrographs or in the time it takes them to peak will be distinguished in the preceding analysis. Following that, the model will be tested against the daily flow data for the periods 1926-1961 and 1987-1997 respectively. It is also expected that individual segments of the network will show varying degrees o f adjustment depending on where they are located within the overall network hierarchy, their relative altitude, the surrounding topography, slope of the main trunk stream, etc.